1. Field of the Invention
The present invention relates to a steering system for vehicles, and particularly, to a steering system for vehicles of the type in which rear wheels are steered in conjunction with the steering operation of front wheels.
2. Description of Relevant Art
There has been proposed, in U.S. Pat. No. 4,412,594, a steering system for vehicles in which rear wheels are steered in conjunction with the steering operation of front wheels, so as to be turned in the same direction as the front wheels at relatively high vehicle speeds and in the opposite direction thereto at relatively low vehicle speeds.
According to the above steering system, at low speeds, the minimum turning radius as well as the trace gap of the inside wheels is greatly decreased, thus remarkably improving the vehicle turning characteristics such as when parking, travelling along a narrow winding road, effecting a U-turn, and driving at high speeds. A homodirectional steering of the rear wheels relative to the front wheels provides enhanced steering responsiveness, so that, for example, lane changes and the like may be performed more adeptly.
Incidentally, while a vehicle is making a turning motion, each grounded wheel of the vehicle is subjected to a certain cornering force (hereinafter called "force Fc") which is a force produced at a grounded portion of a tire to oppose a centrifugal force which appears when the wheel is slipping in accordance with the turning motion, as well known in the relevant art.
The force Fc has such a relation to a slip angle as will be briefly described below with reference to FIGS. 14 to 18 of the accompanying drawings cited from published materials. To simplify the description, forces other than the force Fc are not given in FIGS. 14 to 18 of the drawings, whereas when a grounded wheel is slipping a tire of the wheel is always subjected to a rolling-frictional force and a self aligning torque. Moreover, in the case of a grounded wheel with a camber angle, a camber thrust is acting on the wheel. Further, the grounded wheel undergoes a braking force from time to time, in addition to a drive force to be voluntarily given in the case where the wheel is a drive wheel. In the description, the wheel is assumed to be a wheel with an air-tubed rubber tire.
FIG. 14 is a plan view showing a wheel 400 of a vehicle (not shown), as it is turning. The wheel 400 has a moving direction B thereof deviated from a rolling direction A thereof by a slip angle .beta., or in other words, it is rolling with the slip angle .beta. (hereinafter called "angle.beta.), causing the vehicle to turn clockwise. In such a state, at a grounded surface (not shown) of a tire, due to the friction between a road surface (not shown) and a tread surface (not shown) of the tire, there is produced a centripetal force perpendicular to the moving direction B, that is, in a direction toward the center of turn, which is the force Fc.
As well known, a characteristic on which a tire of a vehicle depends when making a motion with a slip while the vehicle is turning, that is, what is called a cornering characteristic of the tire, is principally governed by such factors as: (1) the material as well as the constitution and configuration of the tire; (2) a vertical load on the tire; (3) an air pressure of the tire; and (4) the condition of the road surface.
With the material as well as the constitution and configuration of the tire now assumed as already given, there will be briefly described a number of relations among other factors (2) and (4) above, the force Fc, and the angle .beta..
FIG. 15 shows a plot of a relation of the force Fc to the angle .beta.. As seen from the plot, although the relation between the force Fc and the angle .beta. is substantially linear when the angle .beta. is small, the ratio of increase in the force Fc to that in the angle .beta. gradually decreases, as the angle .beta. increases beyond a certain value thereof.
With respect to the range in which the Fc vs. .beta. relation is substantially linear, the ratio of an increment .DELTA. Fc of the force Fc to an increment .DELTA..beta. of the angle .beta., that is, .DELTA.Fc/.DELTA..beta., is known as a cornering power K which is an important factor to estimate the cornering characteristic of the tire. The cornering power K varies depending on various conditions such as the air pressure of the tire, a load on the grounded portion of the tire, and the road surface condition.
FIG. 16 provides a plot of a relation between a ratio of the force Fc to the vertical load of the tire represented by W, that is, Fc/W, and the angle .beta.. The vertical load W is known to be always effective in the form of .mu.W on the cornering characteristic, where .mu. is a coefficient of friction of the tire with respect to the road surface, and therefore also the coefficient .mu. of friction has a similar effect thereon, as will be understood from the plot.
FIG. 17 is a graph similar to FIG. 16, while being different therefrom in that the axis of ordinate does not represent the ratio Fc/W, but the force Fc itself. Incidentally, with respect to a grounded wheel adapted to be steerable, the angle .beta. is generally dependent on an actual steering angle and a travelling speed V as well as on other associated conditions. In this respect, when such a wheel is slipping with an angle, the force Fc thereof has a unique value dependent on the angle .beta., provided that such conditions other than the actual steering angle and the travelling speed V are constant, as seen from the graph.
FIG. 18 shows a relation between the cornering power K and the air pressure of the tire as represented by P. As will be understood from this drawing, the cornering power K increases with an increase in the air pressure P, such that the pressure P has a considerable effect on the cornering power K, whereas excessive air pressures will not be substantially effective to increase the cornering power K.
Incidentally, it will also be understood from FIG. 15 that, like the case of the relation to the air pressure P shown in FIG. 18, the cornering power K tends to increase with an increase in the vertical load W, whereas it is also known that excessive loads cause the cornering power K to decrease.
As will be understood from the foregoing description of the cornering characteristic, it is desirable to control the steering of wheels of a steering system according to the before-mentioned relevant art in consideration of various travelling state representative quantities of the wheels.
Concretely speaking, conventional steering systems tend to understeer or oversteer while turning, and it is desirable to eliminate such tendency. Particularly, a vehicle with a conventional steering system tends to slip outwardly at the rear part thereof, thus exhibiting an oversteer effect, when the force Fc of rear wheels is smaller than an ordinary value thereof and, to the contrary, to exhibit an understeer effect when the force Fc is larger than the ordinary value.
Speaking more particularly, it is preferable to make the steering control in consideration of the cornering power K directly representing the relation between the force Fc and the angle .beta., or in other words, taking into account the coefficient .mu. of friction between tire and road surface, the vertical load W, or the air pressure P of the tire, which have their effects on the magnitude of the cornering power K.
From such points of view, the present invention has been achieved to further improve a conventional steering system for vehicles of the above-described type.